Device and method for applying signal weights to signals

Abstract

Signal weights corresponding to an initial system of equations with a block coefficient matrix T 0 can be obtained from the solution to a system of equations with a block coefficient matrix T. The matrix T is approximately equal to the matrix T 0 . The signal weights can be used to generate a desired signal.

1 . A device comprising digital circuits for processing digital signals, wherein said device is a component in one of an imaging device, a sensing device, a communications device, and a general signal processing device, said device further comprising:
 a system transformer for:
 separating a coefficient matrix T into a sum of matrix products, said sum of matrix products comprising matrices C i , wherein said coefficient matrix T is formed from at least one of said digital signals; 
 calculating a transformed coefficient matrix T t  from said matrices C i ; and 
 calculating a transformed vector Y t , wherein said transformed vector Y t  is calculated from at least one of said digital signals; 
   a system solver for determining a solution X from said transformed coefficient matrix T t  and said transformed vector Y t ; and   a system processor for calculating signals J from said solution X.   
   
   
       2 . A device as recited in  claim 1 , wherein said coefficient matrix T is block Toeplitz, and said signals J represent at least one of: a beam pattern, physical characteristics of a target, transmitted speech, images and data, information to control a mechanical, electrical, chemical or biological component, an image, frame of speech and data. 
   
   
       3 . A device as recited in  claim 2 , wherein said coefficient matrix T comprises pad rows and columns. 
   
   
       4 . A device as recited in  claim 2 , wherein said coefficient matrix T comprises modified rows and columns. 
   
   
       5 . A device as recited in  claim 2 , wherein said device further comprises an iterator. 
   
   
       6 . A device as recited in  claim 2 , wherein said system transformer calculates matrices C ti , wherein said matrices C ti  are a fast Fourier transform of said matrices C i . 
   
   
       7 . A device as recited in  claim 6 , wherein said transformed coefficient matrix T t  is calculated from said matrices C ti . 
   
   
       8 . A device as recited in  claim 2 , wherein said sum of matrix products further comprises diagonal matrices D ri . 
   
   
       9 . A method, implemented on a device comprising digital circuits, for determining and applying signal weights to signals J, said signals J representing at least one of: a beam pattern, physical characteristics of a target, transmitted speech, images and data, information to control a mechanical, electrical, chemical, or biological, component, an image, frames of speech and data, said method comprising the steps of:
 forming a coefficient matrix T from input signals;   separating said coefficient matrix T into a sum of matrix products, said sum of matrix products comprising matrices C i ;   calculating a transformed coefficient matrix T t  from said matrices C i ;   calculating a transformed vector Y t  from said input signals;   calculating a solution vector X from said transformed coefficient matrix T t  and said transformed vector Y t ; and   calculating said signals J from said solution X.   
   
   
       10 . A method as recited in  claim 9 , wherein said coefficient matrix T is block Toeplitz, and said device comprising digital circuits is a component in one of an imaging device, a sensing device, a communications device, and a general signal processing device, 
   
   
       11 . A method as recited in  claim 10 , wherein said coefficient matrix T comprises pad rows and columns. 
   
   
       12 . A method as recited in  claim 10 , wherein said coefficient matrix T comprises modified rows and columns. 
   
   
       13 . A method as recited in  claim 10 , said method further comprises calculating iterative updates for said solution vector X. 
   
   
       14 . A method as recited in  claim 10 , said method further comprises calculating matrices C ti , from a fast Fourier transform matrix and said matrices C i . 
   
   
       15 . A method as recited in  claim 14 , said method further comprises calculating said transformed coefficient matrix T t  from said matrices C ti . 
   
   
       16 . A device as recited in  claim 10 , wherein said sum of matrix products further comprises diagonal matrices D ri . 
   
   
       17 . A device comprising digital circuits for processing digital signals, wherein said device is a component in one of an imaging device, a sensing device, a communications device, and a general signal processing device, said device further comprising:
 a system transformer for reducing dimensions of an initial system of equations with a block Toeplitz coefficient matrix T 0  and a vector Y 0 , wherein said coefficient matrix T 0  and said vector Y 0  are formed from input signals;   a system solver for calculating a solution vector X from said coefficient matrix T 0  and said vector Y 0 ; and   a system processor for calculating signals J from said solution vector X, wherein said signals J represent at least one of: a beam pattern, physical characteristics of a target, transmitted speech, transmitted images, transmitted data, information to control a mechanical, electrical, chemical, or biological, component, an image, speech and data.   
   
   
       18 . A device as recited in  claim 17 , wherein said system transformer separates said vector Y 0  into symmetric vectors Y S  and asymmetric vectors Y A , and separates said coefficient matrix T 0  into a symmetric matrix T S  and a skew symmetric matrix T A . 
   
   
       19 . A device as recited in  claim 18 , wherein said system transformer:
 forms systems of equations comprising vectors Y, wherein said vectors Y include said symmetric vectors Y S  and said asymmetric vectors Y A ; and   reduces dimensions of a coefficient matrix T, said coefficient matrix T formed from said symmetric matrix T S  and said skew symmetric matrix T A , by eliminating duplicate elements in said symmetric vectors Y S  and said asymmetric vectors Y A .   
   
   
       20 . A device as recited in  claim 19 , wherein said solution vector X is calculated from a solution to more than one system of equations.